GETTING STARTED 1

In this section we will see, step by step, how to use tiberCAD to simulate numerically a semiconductor device.
As a very simple 1D example we will refer to the Example_0 (Si bulk) that you can find in the examples directory.
See GETTING STARTED 2 for a 2D example.

### Step 1: Modeling the device

As a first step, we have to model the device. To do so, you can use DEVISE module of ISE-TCAD 9.5 software package or GMSH program.
Here we will see in details the procedure for GMSH. There are two possible ways to use GMSH:

1. Interactive, using the graphical interface
2. Using a script file

In the following we’ll see how to write a basic GMSH script (bulk.geo); for any details please refer to GMSH manual GMSH (http://geuz.org/gmsh/).
In a GMSH script, several variables can be defined and given a value in this way:

```L = 1;
d = 0.01;
```

these are valid GMSH variables: L is just the length of the Si sample; d is the value of a characteristic mesh length (see below).

##### - Definition of geometrical entities Points
```Point(1) = {0, 0, 0, d};
Point(2) = {L, 0, 0, d};
```

In the definition of a geometrical point, the three first expressions inside the braces on the right hand side give the three X, Y and Z coordinates of the point; the last expression (d) sets the characteristic mesh length at that point, that is the size of a mesh element, defined as the length of the segment for a line segment, the radius of the circumscribed circle for a triangle and the radius of the circumscribed sphere for a tetrahedron.
Thus, the smaller is the value of d, the greater is the mesh density close to that point. The size of the mesh elements will then be computed in GMSH by linearly interpolating these characteristic lengths in the whole mesh.

N.B.: In a 1D simulation it is assumed that the geometrical model is restricted to the x axis. Any other geometrical orientation could give impredictable results.

##### - Definition of geometrical entity Line

```Line(1) = {1, 2};
```
The two expressions inside the braces on the right hand side give the identification numbers of the start and end points of the line.

##### - Definition of the physical entity Physical Line "bulk"

`Physical Line("bulk") = {1};`
The expression(s) inside the braces on the right hand side give the identification numbers of all the geometrical lines that need to be grouped inside the physical line.

Physical Names are assigned to the Physical entities.
Physical Names consist of strings enclosed between quotation marks.
In this way, in general, physical regions are created which associate together geometrical regions, and then the related mesh elements, which share some common physical properties. It’s only these physical regions which can be referred to outside GMSH.
In tiberCAD, this is done by associating one or more physical regions to a tiberCAD region through the keyword mesh_regions (see in the following).

##### Definition of two physical entities Physical Point

```Physical Point("Anode") = {1};
Physical Point("Cathode") = {2};
```

N.B.: In general, in a nD simulation, (n-1)D physical regions (points in 1D, lines in 2D, surfaces in 3D) are used by TiberCAD to impose the required boundary conditions.
Each (n-1)D physical region defined in this way in GMSH will be associated in tiberCAD to a boundary condition region, through the keyword Contacts. Thus, in this case, Physical points Anode and Cathode will be associated respectively to two Contacts (see in the following).

### Step 2: Meshing the device

The .geo script file with the geometrical description can be run in GMSH, to display the modelled device and to mesh it through the GMSH graphical interface. Alternatively, a non-interactive mode is also available in GMSH, without graphical user interface.
For example, to mesh this 1D tutorial in non-interactive mode, just type:

`gmsh bulk.geo -1 -o bulk.msh`
where
• bulk.geo is the geometrical description of the device with GMSH syntax
• -1 means 1D mesh generation
some command line options are:
• -1, -2, -3 to perform 1D, 2D or 3D mesh generation
• -o mesh_file.msh to specify the name of the mesh file to be generated. In this way, a .msh has been generated and is ready to be read in tiberCAD.

### Step 3: TiberCAD Input file

Now we have to write down the tiberCAD input file (see bulk.tib in Example_0 directory).
For a full reference see End User Guide.

#### 1 - Definition of Device Regions

First, we have to list all the tiberCAD Regions present in our Device: a tiberCAD Region is usually a section of the device featuring the same material and possibly the same doping.

```Device
{
meshfile = bulk.msh
Region bulk
{
material = Si
Doping
{
Nd = 1e16
type = donor
}
}
}
```
The Region bulk is made of Silicon and n-doped with a concentration 1016cm−3.
By defining a Region with the name bulk, we associate the Physical Line "bulk", defined in the Step 1, to the TIBERCAD Region bulk.

Through the keyword mesh_regions, one or more of the physical regions (Physical Lines in 1D, Physical Surfaces in 2D, Physical Volumes in 3D) previously defined in the GMSH mesh can be associated to the present TIBERCAD Region.

#### 2 - Definition of Simulation

Now we define the Simulation driftdiffusion: it belongs to the Module driftdiffusion

```Module driftdiffusion
{
# name = driftdiffusion  # this is the default name
#regions = all # 'all' is the default
# what we want to plot
plot = (Ec, Ev, eQFermi, hQFermi, ContactCurrent)
Contact anode { voltage = \$Vb }
Contact cathode { }
}
```
The TIBERCAD simulation driftdiffusion, belonging to the Module driftdiffusion, will be applied to the whole device structure (physical regions = all ).

#### 3 - Definition of Boundary Conditions

The anode and cathode contacts of our 1D Si sample are defined as Boundary conditions regions (Contact anode, Contact cathode) in the following way

```Contact anode
{
type = ohmic
voltage = @Vb
}
Contact cathode
{
type = ohmic
voltage = 0.0
}
```
Both contacts are defined as ohmic, cathod is assigned a fixed voltage = 0.0, while anode voltage is given by the value of the variable Vb (voltage = @Vb).

Through the keyword mesh_regions, one or more of the (n-1)D physical regions (Physical Points in 1D, Physical Lines in 2D, Physical Surfaces in 3D) previously defined in the GMSH mesh can be associated to the present Contact. With

```Contact Anode
```
we associate the Physical Point Anode, defined in the Step 1, to the Contact anode. With
```Contact Cathode
```
we associate the Physical Point Cathode, defined in the Step 1, to the Contact cathode.

#### 4 - Definition of Simulation parameters

The variable Vb defined in the Contact statement is used in the sweep Module

```Module sweep
{
solve = driftdiffusion
variable = \$Vb
start = 0.0
stop = 1
steps = 10
# for each step we want to plot the solution variables
# specified in the driftdiffusion module
plot_data = true
}
```
In this way, the simulation driftdiffusion is performed for 10 (steps = 10) values of the anode voltage (variable = Vb), between 0 and 1.

#### 5 - Definition of Execution parameters

In the Simulation section , we decide which simulations to perform and in which order;
we set `solve = sweep`, to execute the sweep which run driftdiffusion simulation for the specified loop.

```Simulation
{
# this increases the amount of information
# written to the screen
verbose = 2
solve = sweep
resultpath = output
output_format = grace
}
```
Output files with conduction and valence band profiles (plot = Ec,Ev..) and all the calculated values of the current at the contacts (ContactCurrents) (the IV characteristic) are generated.

`tibercad bulk.tib`